title: Phase separation explains a new class of self-organized spatial patterns in ecological systems.
abstract: The origin of regular spatial patterns in ecological systems has long fascinated researchers. Turing's activator-inhibitor principle is considered the central paradigm to explain such patterns. According to this principle, local activation combined with long-range inhibition of growth and survival is an essential prerequisite for pattern formation. Here, we show that the physical principle of phase separation, solely based on density-dependent movement by organisms, represents an alternative class of self-organized pattern formation in ecology. Using experiments with self-organizing mussel beds, we derive an empirical relation between the speed of animal movement and local animal density. By incorporating this relation in a partial differential equation, we demonstrate that this model corresponds mathematically to the well-known Cahn-Hilliard equation for phase separation in physics. Finally, we show that the predicted patterns match those found both in field observations and in our experiments. Our results reveal a principle for ecological self-organization, where phase separation rather than activation and inhibition processes drives spatial pattern formation.
authors.affiliation: Department of Spatial Ecology, Royal Netherlands Institute for Sea Research, 4400 AC Yerseke, The Netherlands. liuqx315@gmail.com
authors.forename: Quan-Xing
authors.initials: QX
authors.lastname: Liu
authors.forename: Arjen
authors.initials: A
authors.lastname: Doelman
authors.forename: Vivi
authors.initials: V
authors.lastname: Rottschäfer
authors.forename: Monique
authors.initials: M
authors.lastname: de Jager
authors.forename: Peter M J
authors.initials: PM
authors.lastname: Herman
authors.forename: Max
authors.initials: M
authors.lastname: Rietkerk
authors.forename: Johan
authors.initials: J
authors.lastname: van de Koppel
mesh_terms: D063147:Animal Distribution; D000818:Animals; D049872:Bivalvia / Q000502:physiology*; D003198:Computer Simulation; D003710:Demography; D017753:Ecosystem; D008962:Models, Theoretical; D009426:Netherlands; D011156:Population Density
keywords: animal aggregation; mathematical model; mussels; spatial self-organization